As the semiconductor industry moves from its fifth to sixth decade, the continued advancement in agreement with Moore's Law causes many challenges as the lithography enters the sub-10 nm regime (K. Schuegraf, M. C. Abraham, A. Brand, M. Naik and R. Thakur, “Semiconductor logic technology innovation to achieve sub-10 nm manufacturing,” IEEEJ. Electron Device Soc. 1 (2013) 66-75). One major need, which is listed in the roadmaps for the industry, is new means of metrology to provide much greater resolution in profiling the concentration of dopants and carriers. At sub-10 nm lithography the mean spacing for nearest neighbors of the dopant atoms is comparable with the size of each transistor or other components in an integrated circuit. This finer lithography essentially makes a measured average dopant atom concentration insufficient for metrology. Thus, it is essential to distinguish between profiling of the discrete dopant atoms which are at fixed positions and profiling of the mobile carriers which may be considered to be continuous distribution throughout a volume.
Scanning capacitance microscopy (SCM) was introduced in 1989 and this method is still widely used in the semiconductor industry for carrier profiling (C. C. Williams, W. P. Hough and S. A Riston, “Scanning capacitance microscopy on a 25 nm scale,” Appl. Phys. Lett. 55 (1989) 203-205). In SCM, the surface of a semiconductor is coated with a thin layer of oxide and a metal tip is scanned across the surface while in contact with the oxide (C. C. Williams, “Two-dimensional dopant profiling by scanning capacitance microscopy,” Annu. Rev. Mater. Sci. 29 (1999) 471-504). The metal tip is given a negative DC bias relative to the sample for n-type semiconductors, or a positive bias for p-type samples to cause a depletion layer, and the depletion capacitance is measured as a function of the applied bias to determine local values of the carrier concentration as an extension of how this is done in one dimension with capacitance-voltage profiling (J. Hilibrand and R. D. Gold, “Determination of the impurity distribution in junction diodes from capacitance-voltage measurements,” RCA Review. 21 (1960) 245-252). In SCM the total capacitance (depletion layer plus fringing) is measured at high frequencies, typically 915 MHz, which requires a resonant circuit because the changes in the depletion capacitance are typically only 1 part per million of the total capacitance. The finest resolution ever claimed with SCM is 10 nm, and this limit is readily understood because this dimension is comparable with the radius of the metal tip (E. Bussmann and C. C. Williams, “Sub-10 nm lateral spatial resolution in scanning capacitance microscopy achieved with solid platinum probes,” Rev. Sci. Instrum. 75 (2004) 422-425). However, at high resolution it is necessary for the oscillator to drive the semiconductor over the full range from accumulation through inversion to obtain a measurable output signal. Recent “atomistic” simulations confirm the observation that SCM “hits a wall” below 45 nm lithography and is not suitable for carrier profiling with 32 or 22 nm lithography (P. Andrei, M. Mehta and M. J. Hagmann, “Simulations of ‘atomistic’ effects in nanoscale dopant profiling,” Transactions of the 24th Annual SEMI Advanced Semiconductor Manufacturing Conference (ASMC), Saratoga Springs, N.Y., pp. 194-199, 2013).
At the present time scanning spreading resistance microscopy (SSRM) is considered to provide the finest resolution for profiling carriers in semiconductors (A. K. Kambham, J. Mody, M. Gilbert, S. Koelling and W. Vandervorst, “Atom-probe for FinFET dopant characterization,” Ultramicroscopy. 111 (2011) 535-539; 5. Qin, Z. Suo, D. Fillmore, S. Lu, Y. J. Hu and A. McTeer, “Ambient-controlled scanning spreading resistance microscopy measurement and modeling,” Appl. Phys. Lett. 103 (2013) 262105 (3 pp.)). In SSRM the electrical resistance is measured between a sharp conductive probe tip and a large current-collecting back electrode as the probe is inserted into the semiconductor at various points on the surface. When the downward force applied to the probe exceeds a certain threshold, to penetrate the native oxide coating and establish a stable contact, the measured resistance is dominated by the spreading resistance. Diamond is frequently used for the probe tip because of its extreme hardness and high Young's modulus, with electrical conductivity caused by doping. Carrier profiling with a resolution of 1 or 2 nm has been claimed using SSRM but it is unlikely that much finer resolution can be obtained because of the limited strength of materials for the probe tips (L. Zhang, H. Tanimoto, K. Adachi and A. Nishlyama, “l-nm spatial resolution in carrier profiling of ultrashallow junctions by scanning spreading resistance microscopy,” IEEE Electron Device Lett. 29 (2008) 799-801; K. Arstila, T. Hantschel, C. Demeulemeester, A. Moussa and W. Vandervorst, “Microfabricated diamond tip for nanoprobing,” Microelectron. Eng. 86 (2009) 1222-1225; T. Hantschel, C. Demeulemeester, P. Eyben, V. Schulz, O. Richard, H. Bender and W. Vandervorst, “Conductive diamond tips with sub-nanometer electrical resolution for characterization of nanoelectronics device structures,” Phys. Status Solidi A 206 (2009) 2077-2081). Also, SSRM is a destructive process because the surface of the semiconductor is changed by inserting the probe tips, so it is not possible to repeat the measurements at a given location on a sample. It should also be noted that while tips with a radius of only 1 or 2 nm may be fabricated, this dimension is the size of the disruption of the lattice of the semiconductor so the true resolution must be larger than this. As the inserted probe redistributes sample matter, SSRM is also limited in that adjacent insertion points cannot be so close together as to measure resistance at a disturbed locus (from redistribution) or one where the structural integrity has degraded (from the hole left over from the previous test). Also, since the probe is inserted into the semiconductor, it cannot be used in a manner to scan the surface of the semiconductor sample as it cannot move seamlessly across that surface.
The present invention is a method of using a microwave frequency comb to measure microwave attenuation across a volume of a sample in order to determine spreading resistance. When a mode-locked ultrafast laser is focused on the tunneling junction of a scanning tunneling microscope (STM) with a metallic sample, a microwave frequency comb (MFC) is superimposed on the DC tunneling current (M. J. Hagmann, A. Efimov, A J. Talor and D. A. Yarotski, “Microwave frequency-comb generation in a tunneling junction by intermode mixing of ultrafast laser pulses,” App. Phys. Lett. 99 (2011) 011112 (3 pp)). The MFC, which is caused by optical rectification, contains hundreds of measurable harmonics at integer multiples of the pulse repetition frequency of the laser, setting the present state-of-the-art for narrow linewidth at microwave frequencies (M. J. Hagmann, A. J. Taylor and D. A. Yarotski, “Observation of 200th harmonic with fractional linewidth of 10−10 in a microwave frequency comb generated in a tunneling junction,” Appl. Phys. Lett. 101 (2012) 241102 (3 pp); M. J. Hagmann, F. S. Stenger and D. A. Yarotski, “Linewidth of the harmonics in a microwave frequency comb generated by focusing a mode-locked ultrafast laser on a tunneling junction,” J. Appl. Phys. 114 (2013) 223107 (6 pp)).
When using silicon samples in a STM, a MFC at harmonics of the pulse repetition frequency of a Ti:sapphire mode-locked ultrafast laser, independent of whether or not there is a DC tunneling current is seen (M. J. Hagmann, S. Pandey, A. Nahata, A. J. Taylor and D. A. Yarotski, “Microwave frequency comb attributed to the formation of dipoles at the surface of a semiconductor by a mode-locked ultrafast laser,” Appl. Phys. Lett. 101 (2012) 231102 (3 pp)). However, when using SiC or other semiconductors in which the band-gap energy exceeds the photon energy of the laser, there is no frequency comb without a DC tunneling current. This may be understood in that, when the photon energy exceeds the band-gap energy, the laser creates electron-hole pairs in the semiconductor and the motion of these particles causes surge currents at the harmonics. Others have measured terahertz radiation generated by the surge currents, noting that this only occurs when the photon energy exceeds the band-gap energy, but they did not measure the surge currents or appreciate that the terahertz radiation has the structure of a frequency comb (X. C. Zhang and D. H. Auston, “Optoelectronic measurement of semiconductor surfaces and interfaces with femtosecond optics,” J. Appl. Phys. 71 (1992) 326-338).
A laser with photon energy somewhat less than the band-gap energy may cause the electron and hole wave functions to penetrate into the classically forbidden gap to cause “virtual photoconductivity” in what is called the “Inverse Franz-Keldysh effect” (Y. Yafet and E. Yablonovitch, “virtual photoconductivity due to intense optical radiation transmitted through a semiconductor,” Phys. Rev. B 43 (1991) 12480-12489). Terahertz radiation has been generated with this effect by creating virtual carriers with intense femtosecond laser pulses even though the photon energy is less than the band-gap energy of the semiconductor (B. B. Hu, X. C. Zhang and D. H. Auston, “terahertz radiation induced by subband-gap femtosecond optical excitation of GaAs,” Phys. Rev. Lett. 67 (1991) 2709-2712). To summarize, when using lasers with a photon energy less than the band-gap energy of a semiconductor, and moderate values of the power flux density, typically below 1013 W/m2, only the MFC which is caused by optical rectification is seen.
The sequence of four steps in the interaction of the radiation from a femtosecond laser with solids, including semiconductors, has been listed as follows (D. von der Linde, K. Sokolowski-Tinten and J. Bialkowski, “Laser-solid interaction in the femtosecond time regime,” Appl. Surf. Sci. 109 (1997) 1-10):    (1) Primary process: Electrons are excited from their equilibrium states by the absorption of photons, for example, by the creation of electron-hole pairs in a semiconductor when the photon energy is greater than the band-gap energy. The probability of multiphoton processes is more likely with increased laser intensity. The primary process of electronic excitation is associated with a very short-lived coherent polarization of the material having a time scale of about 10 fs.    (2) Dephasing and quasi-equilibrium: There is a complex of secondary processes having different time scales. First dephasing of the polarization of the material occurs at approximately 10 fs. Then the initial distribution of the excited electronic states is rapidly changed by carrier-carrier interaction processes, and quasi-equilibrium is established among the electrons on a time scale of about 100 fs so that the energy distribution of the carriers is described by the Fermi Dirac distribution having an electron temperature that is greater than the lattice temperature.    (3) Cool down by the emission of phonons: The electron temperature of the quasi-equilibrium electrons cools down by the emission of phonons over a time scale of 100 to 1000 fs. These phonons relax predominantly by inharmonic interaction with other phonon modes.    (4) Redistribution of the phonons: The final stage of the thermalization process is the redistribution of the phonons over the entire Brillouin zone according to a Bose-Einstein distribution. At this point the temperature of the laser-excited material can be defined, and the energy distribution is characterized by the temperature. The time scale for this process is typically several picoseconds, and it is followed by thermal diffusion on a time scale of the order of 10 ps.
Several groups have used mode-locked Ti:sapphire lasers to generate femtosecond pulses of electrons (C. Kealhofer, S. M. Foreman, S. Gerlich and M. A. Kasevich, “Ultrafast laser-triggered emission from hafnium carbide tips,” Phys. Rev. B 86 (2012) 035405 (11 pp); M. Kruger, M. Schenk and P. Hommelhoff, “Atosecond control of electrons emitted from a nanoscale metal tip,” Nature 475 (2011) 78-81; H. Yanagisawa, M. Hengsberger, D. Leuenberger, M. Kiockner, C. Hafner, T. Gerber and J. Osterwalder, “Energy distribution curves of ultrafast laser-induced field emission and their implications for electron dynamics,” Phys. Rev. Lett. 107 (2011) 087601 (5 pp); H. Yanagisawa, C. Hafner, P. Dona, M. Klockner, D. Leuenberger, T. Greber, M. Hengsberger and J. Osterwalder, “Optical control of field-emission sites by femtosecond laser pulses,” Phys. Rev. Lett. 103:25 (2009) 257603 (4 pp); C. Ropers, D. R. Solli, C. P. Schultz, C. Lienau and T. Elsaesser, “Localized multiphoton emission of femtosecond electron pulses from metal nanotips,” Phys. Rev. Lett. 98:4 (2007) 043907 (4 pp); P. Hommelhoff, C. Kealhofer and M. A. Kasevich, “Ultrafast electron pulses from a tungsten tip triggered by low-power femtosecond laser pulses,” Phys. Rev. Lett. 97:24 (2006) 247402 (4 pp). Since the center wavelength of 800 nm is not sufficient to cause photoemission with a single photon, the electron emission can only be caused by one or more of the following four processes (C. Kealhofer, S. M. Foreman, S. Gerlich and M. A. Kasevich, “Ultrafast laser-triggered emission from hafnium carbide tips,” Phys. Rev. B 86 (2012) 035405 (11 pp):    (1) Multi-photon emission: When the energy of a single photon is less than the work function of the tip electrode, a number N of photons can liberate an electron across the barrier. For example, multi-photon emission has been observed with N=3 for tungsten and N=4 for gold.    (2) Photo-assisted field emission: When a DC bias is applied to cause field emission, one or more photons can raise the energy of an electron above the Fermi level to increase the probability of barrier penetration in order to increase the emitted current.    (3) Above-threshold photoemission: As the intensity of the optical field is increased, multi-photon processes may occur having higher values of N than the minimum which is required for multi-photon emission.    (4) Transient thermally-enhanced field emission: When a DC bias is applied to cause field emission, heating the tip electrode changes the distribution of energy for the electrons which increases the current. Thus, depending on the heat transfer at the apex of the tip electrode, it is possible for a laser to cause changes in the emitted current at time scales on the order of picoseconds.
Typically the laser pulse has a duration of 15 fs and the pulse repetition frequency is 74.254 MHz, so the spacing between consecutive pulses is approximately 13 ns (M. J. Hagmann, A. Efimov, A. J. Talor and D. A. Yarotski, “Microwave frequency-comb generation in a tunneling junction by intermode mixing of ultrafast laser pulses,” App. Phys. Lett. 99 (2011) 011112 (3 pp); M. J. Hagmann, A. J. Taylor and D. A. Yarotski, “Observation of 200th harmonic with fractional linewidth of 10−10 in a microwave frequency comb generated in a tunneling junction,” Appl. Phys. Lett. 101 (2012) 241102 (3 pp); M. J. Hagmann, F. S. Stenger and D. A. Yarotski, “Linewidth of the harmonics in a microwave frequency comb generated by focusing a mode-locked ultrafast laser on a tunneling junction,” J. Appl. Phys. 114 (2013) 223107 (6 pp). In SFCM, only the use of the laser in a scanning tunneling microscope (STM) with a semiconductor band-gap energy that exceeds the photon energy of the laser is considered. Furthermore, only moderate laser intensity is considered, so that by analogy to the case of laser assisted field emission, the primary process of the four interaction steps can only be photo-assisted tunneling, in which the electrons are raised above the Fermi level to increase the probability of tunneling. The slower processes which take place after each laser pulse are completed before the following pulse, so that it appears that they would have no effect on measurements of the microwave frequency comb.